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Answer:
2 bears in 2020.
Step-by-step explanation:
We have been given that a new bear population that begins with 150 bears in 2000 decreases at a rate of 20% per year.
We will use exponential decay formula to solve our given problem as:
, where,
y = Final quantity,
a = Initial value,
r = Decay rate in decimal form,
x = Time
Upon substituting our given values in above formula, we will get:
, where x corresponds to year 2000.
To find the population in 2020, we will substitute in our equation as:
Therefore, 2 bears are there predicted to be in 2020.
Since population is decreasing so population is best described as exponential decay.
Answer:
And if we find the individual probability we got:
And replacing we got:
Step-by-step explanation:
Previous concepts
The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".
Solution to the problem
Let X the random variable of interest, on this case we now that:
The probability mass function for the Binomial distribution is given as:
Where (nCx) means combinatory and it's given by this formula:
And we want to find this probability:
And we can use the complement rule and we got:
And if we find the individual probability we got:
And replacing we got: